ExploreLearning Gizmos: Math & Science Virtual Labs and Simulations

1: Inferences and Conclusions from Data

1.MCC9-12.S.ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram

1.MCC9-12.S.ID.4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

Polling: City
Populations and Samples
Real-Time Histogram

1.MCC9-12.S.IC.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Polling: City
Polling: Neighborhood
Populations and Samples

1.MCC9-12.S.IC.2: Decide if a specified model is consistent with results from a given data- generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?

Polling: City
Polling: Neighborhood
Populations and Samples

1.MCC9-12.S.IC.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Polling: City
Polling: Neighborhood

1.MCC9-12.S.IC.4: Use data from a sample survey to estimate a population mean or proportion develop a margin of error through the use of simulation models for random sampling.

Polling: City

1.MCC9-12.S.IC.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Polling: City
Polling: Neighborhood

1.MCC9-12.S.IC.6: Evaluate reports based on data.

Describing Data Using Statistics
Polling: City
Polling: Neighborhood
Real-Time Histogram

1.MCC7.SP.1: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that rand om sampling tends to produce representative samples and support valid inferences.

Polling: City
Polling: Neighborhood
Populations and Samples

1.MCC7.SP.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

Polling: City
Polling: Neighborhood
Populations and Samples

1.MCC7.SP.3: Informally assess the degree of visual overlap of two numerical data distributions with similar variability, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram

1.MCC7.SP.4: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations

Box-and-Whisker Plots
Polling: City
Populations and Samples

1.MCC9-12.S.ID.1: Represent data with plots on the real number line (dot plots, histograms, and boxplots).

Box-and-Whisker Plots
Polling: City
Populations and Samples

1.MCC9-12.S.ID.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Box-and-Whisker Plots
Describing Data Using Statistics
Least-Squares Best Fit Lines
Mean, Median, and Mode
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

2: Polynomial Functions

2.MCC9-12.A.SSE.1: Interpret expressions that represent a quantity in terms of its context.

Compound Interest

2.MCC9-12.A.SSE.1a: Interpret parts of an expression, such as terms, factors, and coefficients.

Compound Interest
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

2.MCC9-12.A.SSE.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity

Compound Interest
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

2.MCC9-12.A.SSE.2: Use the structure of an expression to identify ways to rewrite it.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

2.MCC9-12.A.APR.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of x²+bx+c

2.MCC9-12.A.APR.4: Prove polynomial identities and use them to describe numerical relationships.

Factoring Special Products

2.MCC9-12.A.REI.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear and polynomial functions.

Cat and Mouse (Modeling with Linear Systems)
Point-Slope Form of a Line
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Standard Form of a Line

2.MCC9-12.A.APR.2: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x–a is p(a), so p(a) = 0 if and only if (x–a) is a factor of p(x).

Dividing Polynomials Using Synthetic Division

2.MCC9-12.A.APR.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Graphs of Polynomial Functions
Modeling the Factorization of x²+bx+c
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form

2.MCC9-12.F.IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Absolute Value with Linear Functions
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Logarithmic Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions

3: Rational and Radical Relationships

3.MCC9-12.A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from simple rational functions.

Absolute Value Equations and Inequalities
Arithmetic Sequences
Exploring Linear Inequalities in One Variable
Geometric Sequences
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Using Algebraic Equations

3.MCC9-12.A.CED.: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Absolute Value Equations and Inequalities
Circles
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form
Solving Equations on the Number Line
Standard Form of a Line
Using Algebraic Equations

3.MCC9-12.A.REI.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Radical Functions

3.MCC9-12.A.REI.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are rational.

Point-Slope Form of a Line
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Standard Form of a Line

3.MCC9-12..F.IF.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; interval s where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Logarithmic Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Roots of a Quadratic
Slope-Intercept Form of a Line

3.MCC9-12..F.IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

Introduction to Functions
Logarithmic Functions
Radical Functions

3.MCC9-12.F.IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

3.MCC9-12.F.IF.7b: Graph square root, cube root functions.

Radical Functions

3.MCC9-12.F.IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

General Form of a Rational Function
Graphs of Polynomial Functions
Linear Functions
Logarithmic Functions
Quadratics in Polynomial Form
Quadratics in Vertex Form

3.MCC9-12.A.SSE.1a: Interpret parts of an expression by viewing one or more of their parts as a single entity.

Compound Interest
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Equations on the Number Line
Using Algebraic Equations

3.MCC9-12.A.SSE.2: Use the structure of an expression to identify ways to rewrite it.

4: Exponential and Logarithmic Functions

4.MCC9-12.A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II

4.MCC9-12.F.IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

4.MCC9-12.F.IF.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior.

Logarithmic Functions

4.MCC9-12.F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

4.MCC9-12.F.IF.8b: Use the properties of exponents to interpret expressions for exponential functions.

Compound Interest
Exponential Functions

4.MCC9-12.F.BF.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Logarithmic Functions

5: Trigonometric Functions

5.MCC9‐12.F.IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

5.MCC9‐12.F.IF.7e: Graph trigonometric functions, showing period, midline, and amplitude.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

5.MCC9-12.F.TF.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Cosine Function
Sine Function
Tangent Function

5.MCC9-12.F.TF.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

Cosine Function
Sine Function
Tangent Function

5.MCC9-12.F.TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

5.MCC9-12.F.TF.8: Prove the Pythagorean identity (sin A)² + (cos A)² = 1 and use it to find sin A, cos A, or tan A, given sin A, cos A, or tan A, and the quadrant of the angle.

Simplifying Trigonometric Expressions
Sine, Cosine, and Tangent Ratios

6: Mathematical Modeling

6.MCC9-12.A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

6.MCC9-12.A.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

6.MCC9-12.A.CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non‐viable options in a modeling context.

Linear Inequalities in Two Variables
Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

6.MCC9-12.A.CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Area of Triangles
Solving Formulas for any Variable

6.MCC9-12.F.IF.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

6.MCC9-12.F.IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes

Introduction to Functions
Logarithmic Functions
Radical Functions

6.MCC9-12.F.IF.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph

Cat and Mouse (Modeling with Linear Systems)
Slope

6.MCC9-12.F.IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

6.MCC9-12.F.IF.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Slope-Intercept Form of a Line
Standard Form of a Line
Zap It! Game

6.MCC9-12.F.IF.7b: Graph square root, cube root, and piecewise defined functions, including step function s and absolute value functions.

Absolute Value with Linear Functions
Radical Functions
Translating and Scaling Functions

6.MCC9-12.F.IF.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Cosine Function
Logarithmic Functions
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

6.MCC9-12.F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

6.MCC9-12.F.IF.8a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic

6.MCC9-12.F.IF.8b: Use the properties of exponents to interpret express ions for exponential functions.

Compound Interest
Exponential Functions

6.MCC9-12.F.IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

General Form of a Rational Function
Graphs of Polynomial Functions
Linear Functions
Logarithmic Functions
Quadratics in Polynomial Form
Quadratics in Vertex Form

6.MCC9-12.F.BF.1: Write a function that describes a relationship between two quantities.

Points, Lines, and Equations

6.MCC9-12.F.BF.1a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

6.MCC9-12.F.BF.1b: Combine standard function types using arithmetic operations.

Addition and Subtraction of Functions

6.MCC9-12.F.BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k(both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game